POLYLINE

A polyline is a connected sequence of straight line segments formed by joining an ordered list of points in two- or three-dimensional space. Each pair of consecutive points defines a linear edge, and the entire collection of edges constitutes the polyline. A polyline may be open, with distinct endpoints, or closed, in which case it forms a loop. If a closed polyline is simple (its edges do not cross), it is often referred to as a polygon when the interior is well-defined.

In geometry and computer graphics, a polyline represents a polygonal chain used to approximate curves and outlines. It does not inherently enclose an area unless it is closed, and even then it may not define a non-self-intersecting region unless specified as a polygon. A polyline’s shape is fully determined by its sequence of vertices and can be defined in any dimensional space, typically with coordinates such as (x, y) in 2D or (x, y, z) in 3D.

In practice, polylines appear in many domains. In vector graphics and design software, polylines are used to render strokes and paths. In web technology, the SVG polyline element specifies a series of points to draw connected line segments. In geographic information systems and mapping, polylines represent linear features such as roads, rivers, and trails. Common tasks include polyline simplification, smoothing, resampling, and clipping, often to reduce data size or improve rendering performance.